Waves (15)

Variable

Description

 

 

β

Sound level

λ

Wavelength

ω

Angular frequency

ρ

Density of medium

B

Bulk modulus of elasticity

f

Frequency

I

Sound intensity

k

Angular wave number

s

Longitudinal displacement at x and t

sm

Longitudinal amplitude

t

Time

v

Speed of sound in medium (Sound Waves), or

Wave speed (Transverse Waves, Longitudinal

 

Waves)

x

Position

y

Transverse displacement at x and t

ym

Transverse amplitude

 

 

Reference: 3.

Transverse Waves (15,1)

Equations:

y = ym SIN(k x ω ⋅ t)

v = λ ⋅ f

2

⋅ π

ω = 2 ⋅ π ⋅ f

k = ----------

 

 

 

λ

 

Example:

Given: ym=6.37_cm, k=32.11_r/cm, x=.03_cm, ω=7000_r/s, t=1_s.

Solution: f= 1114.0846_Hz, λ=0.0020_cm, y=2.6655_cm, v=218.0006_cm/s.

Longitudinal Waves (15, 2)

Equations:

s = sm COS(k x – ω ⋅ t)

v = λ ⋅ f

2

⋅ π

ω = 2 ⋅ π ⋅ f

k = ----------

 

 

 

λ

 

Example:

Given: sm=6.37_cm, k=32.11_r/cm, x=0.03_cm, ω=7000_r/s, t=1_s.

Solution: s=5.7855_cm, v=2.1800_m/s, λ=0.1957_cm, f=1114.08456_Hz.

Equation Reference 5-59